BAGHDAD — The United Nations said Thursday it is concerned over the plight of civilians caught up in fighting in Iraq’s besieged city of Fallujah, occupied by al-Qaida-linked militants and other Sunni insurgent groups since late December.

The U.N.’s mission to Iraq statement came as security forces intensified shelling inside the city, 40 miles (65 kilometers) west of Baghdad, targeting gunmen holed up inside houses and government buildings. Troops and allied Sunni tribal militias are also trying to drive militants out of parts of nearby Ramadi city, the provincial capital of the western Anbar province.

“I am particularly concerned about the rapidly deteriorating conditions in Fallujah where many residents are caught up in the fighting,” U.N. mission chief Nickolay Mladenov said in the statement. “The UN continues to urge for humanitarian access to the city,” he added.

Residents, who spoke on condition of anonymity for security reasons, said artillery shelling had intensified since last night in a number of the city’s neighborhoods. Some of the shells hit the city’s general hospital, according to its director Wissam al-Essawi. He said that employees would leave the hospital if it is bombed again.

“Hospitals and medical facilities should be protected by all,” Mladenov said.

In his weekly televised speech on Wednesday, Iraqi Prime Minister Nouri al-Maliki said security forces were instructed to differentiate between areas crowded with civilians and those under the control of the militants. But some neighborhoods had turned into “military industrialization” areas, he said.

“Houses, hospitals, schools and other properties are all respected areas, but as we stated before, any house or government building from which a bullet is fired at civilians or the military will be considered a target,” al-Maliki said.

Also Thursday, two bombs, hidden in clothing stalls in the capital’s al-Arabi wholesale market, went off simultaneously, killing six civilians and wounding 18 others, a police and medical official said on condition of anonymity as they were not authorized to brief journalists. Public places such as cafes, restaurants, mosques and markets are favorite targets for militants in Iraq seeking to undermine the Shiite led-government’s efforts to maintain security nationwide.

Iraq is undergoing a surge in violence unseen since 2008 that has become the Shiite-led government’s most serious challenge. Violence has spiked since last April, when security forces cracked down on a Sunni protest camp north of Baghdad in clashes that left 45 dead. According to the U.N., 8,868 people were killed in Iraq last year — the country’s highest death toll since a peak of sectarian bloodletting in 2007.